Unit 8- Dilations

Vocabulary 1

100

Dilation

What transforms an object by enlarging or reducing it

200

Scale Factor

What effects the dilation

300

Quadrilateral

What is a four sided figure

400

Line Segment

What is a part of a line bounded by two distinct end points

500

Origin

What is the point where lines intersect

Vocabulary 2

100

Parallel

What are lines that have the same distance between them continuously

200

Polygon

What is a plane figure with at least three straight sides and angles

300

Transformation

What are changes made to any given figure

400

Pre-image

What is the original appearance of a figure in a transformation operation

500

Vertices

What are the points where two or more line segments or edges meet

Formulas

100

Slope-Intersect Formula

What is y=mx+b

200

Distance Formula

What is √(x₂-x₁)² + (y₂-y₁)²

300

r_y-axis

What is (x,y) —> (-x,y)

400

r_x-axis

What is (x,y) —> (x,-y)

500

Dilation Rule

What is (x,y) —> (rx, ry)

Questions 1

100

A right triangle is dilated by a scale factor of 1/4, what is the scale factor of the area of the image?

1/16

200

Triangle A’B’C’ is the image of Triangle ABC after a dilation of 2. Which of the following statements is true?

(1) AB = A’B’

(2) BC = 2(B’C’)

(3) 2(BC) = B’C’

(4) m∠B = 2(m∠B’)

3

300

A rectangle is dilated by a scale factor. The dilated image has an area that is 16 times greater than the  original image. Find the scale factor of the perimeters from the pre-image to the image.

Original scale factor = 4

400

What is the image (3,-2) under the dilation of D₅

(15,-10)

500

The image point after a dilation of 1/2 is (3,-2), what is the pre-image point?

(6,-4)

Questions 2

100

Determine the scale factor of a dilation if the coordinates of A are (5,-2) and the coordinates of A’ are (-10,4)

Scale factor = -2

200

 The line  2x + 3y = 0  is dilated by a scale factor of 3 and centered at the origin. What is the equation of its image in slope-intercept form?

y= -2/3x

300

 The line  y = 3x − 4  is dilated by a scale factor of 2 with a center at  C(1, −1).  What is the equation of its image?

y=3x-4

400

A line segment that passes through the points whose coordinates are  (−1,4)  and  (5, −2)  is dilated by  a scale factor of 2 and centered at  (1,2). The image of the line 

(1) is perpendicular to the original line segment 

(2) is parallel to the original line segment 

(3) passes through the origin 

(4) is the original line segment

2

500

If the line represented by y=-1/4x-2 is dilated by a scale factor of 4 centered at the origin, which statement about the image is true?

(1) the slope is -1/4 and the y-intercept is -8

(2) the slope is -1/4 and the y-intercept is -2

(3) the slope is -1 and the y-intercept is -8

(4) the slope is -1 and the y-intercept is -2

1